Ladder representations and Galois distinction

Date(s) : 06/01/2015   iCal
14 h 30 min - 15 h 30 min

The space X=GL_n(E)/GL_n(F), for a quadratic extension E/F of p-adic fields, serves as an approachable case for the study of harmonic analysis on p-adic symmetric spaces on one hand, while having ties with Asai L-functions on the other. The smooth irreducible representations of GL_n(E) which can be embedded as functions on X are called GL_n(F)-distinguished. It is known that a GL_n(F)-distinguished representation must be contragredient to its own Galois conjugate. Conversely, a conjecture often attributed to Jacquet states that the last-mentioned condition is close to being sufficient for distinction. We show the conjecture is valid for the class of ladder representations which was recently explored by Lapid and Minguez. Along the way, we suggest a reformulation of the conjecture which concerns standard modules in place of irreducible representations.

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